EX-5.1

Exhibit 5.1

[LETTERHEAD OF WACHTELL, LIPTON, ROSEN & KATZ]

November 19, 2021

Triumph Bancorp, Inc.

12700 Park Central Drive, Suite 1700

Dallas, Texas 75251

Ladies and Gentlemen:

We have acted as special counsel to Triumph Bancorp, Inc. (the “Company”), a Texas corporation, in connection with the registration, pursuant to a registration statement on Form S-4 (the “Registration Statement”), initially filed by the Company with the U.S. Securities and Exchange Commission under the U.S. Securities Act of 1933, as amended (the “Act”), on November 19, 2021, relating to the proposed offer by the Company to exchange (the “Exchange Offer”) an aggregate principal amount of up to $70,000,000 of 3.500% Fixed-to-Floating Rate Subordinated Notes due 2031 (the “Old Notes”) for an equal principal amount of the Company’s registered 3.500% Fixed-to-Floating Rate Subordinated Notes due 2031 (the “Exchange Notes”), the exchange of which will be registered under the Act. The Company is proposing to conduct the Exchange Offer in accordance with the terms of Registration Rights Agreements with respect to the Old Notes dated as of August 26, 2021 by and among the Company and the initial purchasers of the Old Notes.

The Old Notes were issued, and the Exchange Notes will be issued, under the Indenture, dated as of September 30, 2016 (the “Base Indenture”), by and between the Company and Wells Fargo Bank, National Association as trustee as amended and supplemented by the Third Supplemental Indenture, dated as of August 26, 2021 (the “Third Supplemental Indenture”). We refer to the Base Indenture, as amended and supplemented by the Third Supplemental Indenture, as the “Indenture.”

In rendering the opinions expressed in this letter, we have examined the Registration Statement, the Indenture, the forms of the Exchange Notes, and originals or copies certified or otherwise identified to our satisfaction of such other documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or appropriate for the purposes of this letter. The Exchange Notes and the Indenture are referred to herein as the “Transaction Documents.”

We have also conducted such investigations of fact and law as we have deemed necessary or advisable for purposes of this letter. In such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all documents submitted to us as copies and the legal capacity of all individuals executing such documents. As to any facts material to the opinions expressed below, we have, with your consent, relied upon the statements, certificates and representations of officers and other representatives of parties to the Transaction Documents and of the Company. We have also assumed (i) the valid authorization, execution and delivery of the Transaction

Documents by each party thereto, (ii) that each such other party (in the case of parties which are not natural persons) has been duly organized and is validly existing and in good standing under its jurisdiction of organization, (iii) that each such other party has the legal capacity, power and authority to perform its obligations thereunder and (iv) that each of the Transaction Documents constitutes the valid and binding obligation of each party thereto, enforceable against it in accordance with its terms (other than as expressly covered by our opinions below in respect of the Company ). We have also assumed that the execution, delivery and performance of the Transaction Documents by each party thereto have been duly authorized by all necessary action (corporate or otherwise) and do not (x) contravene its respective certificate or articles of incorporation, limited liability company agreement, bylaws or other organizational documents, (y) violate any law, rule or regulation applicable to it, or (z) result in any conflict with, or breach of any agreement or document binding on it. In addition, the enforceability of indemnification and contribution provisions may be limited by applicable law and public policy considerations. Furthermore, the manner in which any particular issue relating to the opinions would be treated in any actual court case would depend in part on facts and circumstances particular to the case and would also depend on how the court involved chose to exercise the wide discretionary authority generally available to it.

We are members of the Bar of the State of New York, and we have not considered, and we express no opinion as to, the laws of any jurisdiction other than the laws of the State of New York that a New York lawyer exercising customary professional diligence would reasonably be expected to recognize as being applicable to the Company, the Transaction Documents or the transactions governed by the Transaction Documents, in each case as in effect on the date hereof (the “Relevant Laws”). Without limiting the generality of the foregoing definition of Relevant Laws, the term “Relevant Laws” does not include any law, rule or regulation that is applicable to the Company and the Transaction Documents or such transactions solely because such law, rule or regulation is part of a regulatory regime applicable to any party to any of the Transaction Documents or any of its affiliates due to the specific assets or business of such party or such affiliate.

Insofar as the opinions expressed herein relate to or are dependent upon matters governed by the laws of the State of Texas, we have relied upon the opinion letter, dated the date hereof, of Adam D. Nelson, the Company’s Executive Vice President and General Counsel, which opinion letter is being filed as an exhibit to the Registration Statement, and our letter is subject to the same assumptions, qualifications and limitations with respect to such matters as are contained in such letter.

Based upon the foregoing, and subject to the qualifications set forth in this letter, it is our opinion that when (i) the Registration Statement has become effective under the Act, (ii) the Old Notes have been exchanged in the manner described in the prospectus forming a part of the Registration Statement, (iii) the Exchange Notes have been duly executed, authenticated, issued and delivered by the Company in accordance with the terms of the Indenture, against receipt of the Old Notes surrendered in exchange therefor, (iv) the Indenture has been duly qualified under the Trust Indenture Act of 1939, as amended, and (v) applicable provisions of “blue sky” laws have been complied with, the Exchange Notes proposed to be issued pursuant to the Exchange Offer will constitute valid and legally binding obligations of the Company, except as may be limited by applicable bankruptcy, insolvency, fraudulent conveyance, fraudulent transfer, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights or remedies generally and by general equitable principles (whether considered in a proceeding in equity or at law).

The opinions expressed herein are subject to the following qualifications and comments:

a) Any provisions of the Transaction Documents that permit any party thereto to take action or make determinations, or to benefit from indemnities and similar undertakings of any party to the Transaction Documents, may be subject to a requirement that such action be taken or such determinations be made, and any action or inaction by such party that may give rise to a request for payment under such an undertaking be taken or not taken, on a reasonable basis and in good faith.

b) We express no opinion as to (i) whether a federal or state court outside New York would give effect to any choice of law provided for in the Transaction Documents, (ii) any provisions of the Transaction Documents that relate to the subject matter jurisdiction of the federal or state courts of a particular jurisdiction to adjudicate any controversy related to the Transaction Documents or the transactions contemplated thereby, (iii) any waiver of inconvenient forum set forth in the Transaction Documents or (iv) any waiver of jury trial found in the Transaction Documents.

We hereby consent to the filing of a copy of this letter as an exhibit to the Registration Statement and to the use of our name in the prospectus forming a part of the Registration Statement under the caption “Legal Matters.” In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act and the rules and regulations thereunder. This letter speaks as of its date, and we undertake no (and hereby disclaim any) obligation to update this letter.

Very truly yours,

/s/ Wachtell, Lipton, Rosen & Katz